By Eckhard Meinrenken
This monograph offers an advent to the speculation of Clifford algebras, with an emphasis on its connections with the idea of Lie teams and Lie algebras. The ebook starts off with an in depth presentation of the most effects on symmetric bilinear varieties and Clifford algebras. It develops the spin teams and the spin illustration, culminating in Cartan’s well-known triality automorphism for the crowd Spin(8). The dialogue of enveloping algebras encompasses a presentation of Petracci’s facts of the Poincaré–Birkhoff–Witt theorem.
This is through discussions of Weil algebras, Chern--Weil concept, the quantum Weil algebra, and the cubic Dirac operator. The functions to Lie conception contain Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The final a part of the publication is an account of Kostant’s constitution idea of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his interesting conjecture concerning the Harish-Chandra projection for Clifford algebras to the imperative sl(2) subalgebra.
Aside from those attractive purposes, the booklet will function a handy and updated reference for historical past fabric from Clifford concept, proper for college students and researchers in arithmetic and physics.
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Additional info for Clifford Algebras and Lie Theory: 58 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
Clifford Algebras and Lie Theory: 58 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Eckhard Meinrenken